Simplify (1-tan(x)^2)/(cot(x)^2-1)

$\frac{1 - \tan^{2} (x)}{\cot^{2} (x) - 1}$

Simplify the numerator.

Rewrite $1$ as $1^{2}$ .

$\frac{1^{2} - \tan^{2} (x)}{\cot^{2} (x) - 1}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = \tan (x)$ .

$\frac{(1 + \tan (x)) (1 - \tan (x))}{\cot^{2} (x) - 1}$

Simplify the denominator.

Rewrite $1$ as $1^{2}$ .

$\frac{(1 + \tan (x)) (1 - \tan (x))}{\cot^{2} (x) - 1^{2}}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \cot (x)$ and $b = 1$ .

$\frac{(1 + \tan (x)) (1 - \tan (x))}{(\cot (x) + 1) (\cot (x) - 1)}$

Simplify (1-tan(x)^2)/(cot(x)^2-1)

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